Preamble

Vol. 43, No. 3

September, 2025

Progress in Astronomy

doi: 10.3969/j.issn.1000-8349.2025.03.05

Investigating the Ages of R-Process Enhanced Metal-Poor Stars Using Th/U Nuclear Chronometry

LONG Yin¹, CHEN Menghua²

(1. School of Mathematics and Physics, Hechi University, Hechi 546300, China;
2. Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China)

Abstract

Metal-poor stars are ancient stars formed in the early universe that preserve the chemical signatures of early nucleosynthesis, providing crucial clues for studying heavy element synthesis mechanisms and the chemical evolution of the early cosmos. Using Th/U nuclear chronometry, we analyzed the ages of eight known r-process enhanced metal-poor stars: CS31082-001, BD+17°3248, HE1523-0901, CS29497-004, J2038-0023, J0954+5246, J2003-1142, and J2213-5137. The results show that these eight r-process enhanced metal-poor stars have ages ranging from 7.4 to 16.9 Gyr, with a mean age of 13.2 Gyr. None of these stellar ages significantly exceed the cosmic age of 13.8 Gyr inferred from cosmic microwave background radiation, providing independent support for the Big Bang theory. The primary source of uncertainty in Th/U nuclear chronometry stems from uncertainties in both the initial and observed abundances of thorium and uranium.

Keywords: Th/U nuclear chronometry; metal-poor star; r-process

1. Introduction

According to nucleosynthesis theory, heavy elements are produced primarily through two processes: the rapid neutron-capture process (r-process) and the slow neutron-capture process (s-process). The r-process is considered the main pathway for synthesizing heavy elements, accounting for more than half of all heavy elements in the universe, including all thorium (Th) and uranium (U) elements [1, 2]. During the r-process, atomic nuclei rapidly capture multiple neutrons to form neutron-rich isotopes. These neutron-rich isotopes are typically unstable and undergo β-decay, increasing their atomic number to produce heavier elements, which can then continue to capture neutrons to synthesize even heavier elements. The r-process not only explains the abundance patterns of r-process heavy elements in the solar system but also matches observational results of heavy element abundances in metal-poor stars [2].

Fowler received the Nobel Prize in Physics in 1983 for his outstanding contributions to the theory of heavy element nucleosynthesis. The r-process requires extreme conditions—high temperature, high density, and high neutron flux. Numerous simulation studies have shown that two astrophysical environments can satisfy these nuclear reaction conditions: (1) core-collapse supernova explosions, and (2) binary neutron star mergers or neutron star–black hole mergers. Further research has revealed that during core-collapse supernovae, the relatively low neutron abundance can only synthesize some of the lighter r-process elements [3]. In contrast, during binary neutron star mergers, material is ejected through tidal centrifugal forces, collisional compression, and accretion feedback. These ejecta contain large numbers of free neutrons and can produce substantial quantities of heavy elements through the r-process [4]. Consequently, binary neutron star mergers are considered ideal sites for the r-process [5].

On August 17, 2017, the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected the first gravitational wave signal from a neutron star merger event (GW170817) [6]. Subsequent multi-wavelength, multi-messenger follow-up observations revealed an associated gamma-ray burst (GRB170817A) and kilonova emission (AT2017gfo) [7]. By analyzing the light curves and spectral energy distributions of the kilonova radiation, scientists inferred that this event synthesized approximately 0.05 M⊙ of heavy elements [8]. Furthermore, they obtained the first direct evidence for the presence of the heavy element strontium in the spectrum [9]. A research team from Peking University analyzed the occurrence rate of neutron star merger events and the yield of heavy elements per event, finding that these events can not only reproduce the observed characteristics of r-process elements in the solar system but also successfully explain the total observed abundance of heavy elements in the Milky Way [10]. These results demonstrate that neutron star merger events are the primary sites of the r-process and an important source of heavy elements in the universe.

After heavy elements are synthesized in neutron star merger events, they are ejected into the interstellar medium and contribute to the formation of subsequent generations of stars. The abundance patterns of these heavy elements are preserved in some ancient stars, such as r-process enhanced metal-poor stars [11]. R-process enhanced metal-poor stars are stars that formed early in the universe with low metallicity but are enriched in r-process elements. Since these stars retain the chemical signatures of early nucleosynthesis, they provide key clues for studying the nucleosynthesis mechanisms of the r-process and the chemical evolution of the early universe. To accurately determine the ages of these metal-poor stars, scientists typically employ the Th/U nuclear chronometry method. This method utilizes the radioactive decay of thorium and uranium isotopes: the half-life of ²³²Th is approximately 14 Gyr, while that of ²³⁸U is about 4.5 Gyr. By measuring the initial and observed abundance ratios of these two isotopes and combining them with their radioactive decay law, the ages of metal-poor stars can be calculated. This method provides important evidence for studying the formation history and early evolution of stars. Additionally, Th/Eu or U/Eu nuclear chronometry can be used to determine the ages of metal-poor stars. Notably, Th and U are pure r-process elements that can only be synthesized through the r-process, whereas Eu synthesis is influenced by both s- and r-processes, introducing significant uncertainties in age calculations. Recently, a research team from the National Astronomical Observatories of China discovered an r-process enhanced star with extremely high Eu abundance using the Guo Shoujing Telescope (LAMOST) [12], suggesting that Eu in stars may have complex formation mechanisms and enrichment processes. Moreover, Th (atomic number 90) and U (atomic number 92) are neighboring elements, and their abundance ratio is relatively insensitive to astrophysical environmental parameters and nuclear physics inputs. In contrast, Eu (atomic number 63) is far from Th and U in atomic number, which may lead to larger systematic errors. Therefore, Th/U nuclear chronometry is an independent dating method based on nuclear decay laws that does not rely on galactic evolution models and is suitable for determining the ages of metal-poor stars [13].

As of September 2024, scientists have discovered eight r-process enhanced metal-poor stars with observed Th and U data: CS31082-001 [14], BD+17°3248 [15], HE1523-0901 [16], CS29497-004 [17], J2038-0023 [18], J0954+5246 [19], J2003-1142 [20], and J2213-5137 [21]. These stars have extremely low metallicity ([Fe/H] < −2.0), indicating they formed in the early universe. Additionally, all eight metal-poor stars exhibit prominent r-process element absorption line features, indicating they experienced significant r-process enrichment in the early cosmos. This paper employs Th/U nuclear chronometry to analyze the ages of these eight r-process enhanced metal-poor stars.

2. Methods

According to the radioactive decay law, the relationship between the number of remaining nuclei 𝑁(𝑡) after time 𝑡 and the initial number 𝑁(0) can be expressed as:

where 𝜆 is the decay constant. For the radioactive decay of ²³²Th and ²³⁸U, this can be expressed respectively as:
𝑁(𝑡) = 𝑁(0) exp(−𝜆𝑡)
𝑁Th(𝑡) = 𝑁Th(0) exp(−𝜆Th𝑡)
𝑁U(𝑡) = 𝑁U(0) exp(−𝜆U𝑡)

Combining these expressions, we obtain:
𝑁U(𝑡) 𝑁Th(𝑡) = 𝑁U(0) 𝑁Th(0) exp[−(𝜆U − 𝜆Th)𝑡]

Taking the logarithm of both sides yields:
lg 𝑁U(𝑡) 𝑁Th(𝑡) = lg 𝑁U(0) 𝑁Th(0) − (𝜆U − 𝜆Th)𝑡 lg e

Simplifying this expression gives:
(𝜆U − 𝜆Th) lg e 𝑁U(0) 𝑁Th(0)

The relationship between the half-life 𝑇1/2 and decay constant 𝜆 is given by 𝑇1/2 = 𝑁U(𝑡) 𝑁Th(𝑡). According to the NuDat3.0 database from the National Nuclear Data Center, the half-lives of the radioactive isotopes ²³²Th and ²³⁸U are 14.07 Gyr and 4.46 Gyr, respectively. Substituting these values into the equation and simplifying, the age of a metal-poor star can be expressed as:
𝑡 = 21.71

where 𝑡 is in units of Gyr, and (U/Th)ini and (U/Th)obs represent the initial and observed abundance ratios of U to Th, respectively.

Based on this age formula for metal-poor stars, determining stellar ages using Th/U nuclear chronometry requires knowledge of both the initial and observed U/Th abundance ratios. Bauswein et al. [22] simulated r-process nucleosynthesis in neutron star merger events and found that the Th/U abundance ratio is approximately 1.7, corresponding to lg(U/Th)ini = −0.23. Frebel et al. [16] considered the effects of astrophysical parameters on r-process nucleosynthesis and obtained a range of lg(U/Th)ini = −0.22 to −0.30, consistent with Bauswein et al.'s results. Therefore, in this work we adopt lg(U/Th)ini = −0.26 ± 0.04.

3. Results and Analysis

Figure 1 [FIGURE:1] shows the heavy element abundances of the eight metal-poor stars, with the solid black line representing r-process element abundances in the solar system. The figure demonstrates that the heavy element abundance patterns of these eight stars are consistent with solar r-process abundances, indicating they experienced significant r-process enrichment in the early universe. Consequently, Th/U nuclear chronometry can be applied to determine their ages. Figure 2 [FIGURE:2] presents the metallicities and observed U/Th abundance ratios of the eight r-process enhanced metal-poor stars. The observed lg(U/Th)obs values range from −1.1 to −0.6. Three stars have observational uncertainties of ±0.30: BD+17°3248, CS29497-004, and J2213-5137, while CS31082-001 has a smaller uncertainty of ±0.11.

Note: The horizontal axis represents atomic number, and the vertical axis shows observed heavy element abundances. The solid black line indicates solar r-process element abundances from reference [23]. Stellar abundances are normalized to 𝑌(Eu) = 4.5 × 10⁻⁵.

Using the Th/U nuclear chronometry age formula, we calculated the ages of the eight r-process enhanced metal-poor stars, as shown in Figure 3 [FIGURE:3]. The shaded region indicates the error range due to the initial abundance (U/Th)ini, while error bars represent uncertainties from the observed abundance (U/Th)obs. For a given initial abundance ratio, stellar age shows a linear relationship with the observed abundance ratio lg(U/Th)obs: as the age increases, the absolute value of lg(U/Th)obs also increases. The ages of these eight stars range from 7.4 to 16.9 Gyr, with a mean age of 13.2 Gyr. In r-process nucleosynthesis simulations, the initial abundance ratio is lg(U/Th)ini = −0.26 ± 0.04, yielding an age uncertainty of 0.9 Gyr from the initial abundance. The figure shows that uncertainties from observed abundances (U/Th)obs are significantly larger than those from initial abundances (U/Th)ini. CS31082-001 has the smallest uncertainty, with an age error of only 2.4 Gyr from observational abundances, while CS29497-004 has the largest uncertainty, reaching 7.2 Gyr. These results indicate that precise analysis of observed Th and U abundances in r-process enhanced metal-poor stars will effectively reduce age calculation uncertainties. Additionally, accurate evaluation of Th and U initial abundances using high-precision r-process nucleosynthesis codes will help minimize uncertainties.

Note: The shaded region indicates the error range from initial abundance (U/Th)ini, while error bars show uncertainties from observed abundance (U/Th)obs.

Figure 4 [FIGURE:4] presents the age calculations for the eight r-process enhanced metal-poor stars, with error bars incorporating uncertainties from both initial and observed abundances. Among the eight known r-process enhanced metal-poor stars, the oldest is CS29497-004 at 16.9 ± 8.0 Gyr, while the youngest is J2003-1142 at 7.4 ± 5.2 Gyr. The star with the smallest uncertainty is CS31082-001, with an age of 14.8 ± 3.3 Gyr. No clear correlation exists between stellar age and metallicity [Fe/H]. Table 1 [TABLE:1] lists the age calculations and error ranges for all eight stars.

Figure 4 also compares these stellar ages with the cosmic age inferred from cosmic microwave background radiation. Since substantial evolutionary time is required from the birth of the universe to the formation of r-process enhanced metal-poor stars, their ages should be younger than the cosmic age. Therefore, Th/U nuclear chronometry serves as an independent dating method that can determine a lower limit for the cosmic age by measuring ancient stellar ages, thereby providing strong evidence for the Big Bang theory. The figure shows that the ages of these early-forming r-process enhanced metal-poor stars do not significantly exceed the cosmic age from cosmic microwave background radiation within their error bounds. This result demonstrates that ages determined via Th/U nuclear chronometry provide independent support for the cosmic age inferred from cosmic microwave background radiation.

We compared our age determinations with those estimated by Wu et al. [25], as shown in Figure 5 [FIGURE:5]. Wu et al. analyzed six r-process enhanced metal-poor stars using r-process nucleosynthesis simulations, excluding the recently discovered stars J2003-1142 and J2213-5137. The figure shows that ages determined via Th/U nuclear chronometry are consistent with results from r-process nucleosynthesis simulations. Our work also analyzed the two recently discovered stars J2003-1142 and J2213-5137, yielding ages of 7.381 ± 5.210 Gyr and 15.197 ± 7.164 Gyr, respectively.

Note: Yellow indicates results from this work; blue indicates results from Wu et al. [25].

4. Summary and Discussion

Using Th/U nuclear chronometry, we investigated the ages of eight known r-process enhanced metal-poor stars: CS31082-001, BD+17°3248, HE1523-0901, CS29497-004, J2038-0023, J0954+5246, J2003-1142, and J2213-5137. Analysis of their heavy element abundances reveals observed U/Th abundance ratios lg(U/Th)obs ranging from −1.1 to −0.6. Applying the Th/U nuclear chronometry age formula, we calculated ages for these eight stars, finding a range of 7.4 to 16.9 Gyr with a mean age of 13.2 Gyr. Our Th/U chronometry ages are consistent with results from r-process nucleosynthesis simulations by Wu et al.

Th/U nuclear chronometry is an independent dating method that avoids uncertainties introduced by galactic evolution models. By determining the ages of ancient stars, this method can effectively establish a lower limit for the cosmic age. In this work, ages of r-process enhanced metal-poor stars determined via Th/U chronometry do not significantly exceed the cosmic age from cosmic microwave background radiation within their error bounds, providing independent evidence supporting the Big Bang theory.

We also analyzed the sources of uncertainty in Th/U nuclear chronometry. The primary uncertainties originate from two aspects: (1) the initial abundance ratio of Th and U, and (2) the observed abundance ratio of Th and U. For most metal-poor stars, uncertainties from observed abundance ratios are significantly larger than those from initial abundance ratios. Therefore, precise analysis of observed Th and U abundances in r-process enhanced metal-poor stars will effectively reduce age calculation uncertainties. Additionally, accurate evaluation of Th and U initial abundances using high-precision r-process nucleosynthesis codes will help minimize uncertainties in age determinations.

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